Do I need to atmospherically correct the Sentinel-2 Level 1C data in order to calculate NDVI or other such indices?

I have downloaded sen2cor for doing atmospheric correction of ToA reflectance images of Sentinel-2 level 1C data. But do I really need Bottom of Atmosphere reflectance values (surface reflectance) for NDVI comparison purposes of time series data?

especially if you want to compare NDVI values of multiple dates, radiometric correction is required.
For some areas, L2A data can be downloaded already. For all others, you can process them to reflectance with sen2cor.


if the area is steepy and many effect of ridge shadows, I think it is necessary to do atmospheric and surface correction. Otherwise your NDVI will vary according to ridge direction.